If \( \left|\begin{array}{lll}x+y & y+z & z+x \\ y+z & ...

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If \( \left|\begin{array}{lll}x+y & y+z & z+x \\ y+z & z+x & x+y \\ z+x & x+y & y+z\end{array}\right|=k\left|\begin{array}{lll}x & z & y \\ y & x & z \\ z & y & x\end{array}\right| \), then \( k \) is equal to
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